[EM] Head to Head Comparison of Election Methods

DEMOREP1 at aol.com DEMOREP1 at aol.com
Wed Jun 9 19:52:50 PDT 1999

Mr. Dumais wrote in part on June 8 --

Good point. I've assumed any table can be achieved with a set of
votes (how wrong I was!). Producing the examples I'm looking for might
be difficult, but this is primarily because they occur with 4 or more
candidates. Does anyone have a good way of producing voting examples
given a pair-wise matrix? It is not as trivial as I had first assumed.
Going backward from a head to head table with N choices to actual votes (such 
as X votes for  B > C > A > D > M > N > T ) is a major chore since there are 
N factorial possibilities of combinations of ranked votes (ignoring truncated 
votes) ---

Choices    Factorial
2                2 x 1 = 2   (A > B or B > A)
3                3 X 2 x1 = 6
4                4 x 3 x 2 x 1 = 24  (first chance for clones in tie cases 
with no head to head winner)
5               120
6               720
7               5040
etc.            etc.

Any supercomputer programmers in internet land (especially for testing 
methods with a 6 or more choices) ???

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